Question

A man wearing a hat of extended length $12cm$ is running in rain falling vertically downwards with speed $10m/s$. The maximum speed with which man can run, so that rain drops do not fall on his face (the length of his face below the extended part of the hat is $16cm$) will be

• A. $7.5m/s$
• B. $13.33m/s$
• C. $10m/s$
• D. $0m/s$

Answer 1

The correct option is A $7.5m/s$

$V_{rain}=10m/s$ (in negative $y$ direction)
Let, velocity of man = $v$
Also from the above diagram we get the value of $\theta$ as
$tan\theta =\frac{16}{12}=\frac{4}{3}$
then, velocity of rain w.r.t man $V_{rain/man}$= $v$ (opposite to man i.e. in negative $x$ direction)
For the required condition :
$tan\theta =\frac{10}{v}=\frac{4}{3}$
or
$v=\frac{10\times 3}{4}=7.5$